In this thesis some fundamental theoretical problems about artificial neural networks and their application in communication and control systems are discussed. We consider the convergence properties of the Back-Propagation algorithm which is widely used for training of artificial neural networks, and two stepsize variation techniques are proposed to accelerate convergence. Simulation results demonstrate significant improvement over conventional Back-Propagation algorithms. We also discuss the relationship between generalization performance of artificial neural networks and their structure and representation strategy. It is shown that the structure of the network which represent a priori knowledge of the environment has a strong influence on generalization performance. A Theorem about the number of hidden units and the capacity of self-association MLP (Multi-Layer Perceptron) type network is also given in the thesis. In the application part of the thesis, we discuss the feasibility of using artificial neural networks for nonlinear system identification. Some advantages and disadvantages of this approach are analyzed. The thesis continues with a study of artificial neural networks applied to communication channel equalization and the problem of call access control in broadband ATM (Asynchronous Transfer Mode) communication networks. A final chapter provides overall conclusions and suggestions for further work.